The paper describes RO(C_2×Σ_2) cohomology properties, computing subrings of motivic classes and their implications.
We describe the main properties of the RO(C₂× Σ ₂) R O ( C 2 × Σ 2 ) -graded cohomology ring of a point and apply the results to compute the subring of motivic classes given by the Bredon motivic cohomology of real numbers and to compute RO(C₂× Σ ₂) R O ( C 2 × Σ 2 ) -graded cohomology ring of EΣ ₂C₂ E Σ 2 C 2 . This generalizes Voevodsky’s identification of motivic cohomology of real numbers with the positive cone of RO(C₂) R O ( C 2 ) graded cohomology of a point.
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Deng et al. (2026) studied this question.
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